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## App Honors Calc IV

by: Mrs. Preston Lehner

18

0

1

# App Honors Calc IV MATH 256

Mrs. Preston Lehner
UM
GPA 3.87

Jeffrey Rauch

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COURSE
PROF.
Jeffrey Rauch
TYPE
Class Notes
PAGES
1
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 1 page Class Notes was uploaded by Mrs. Preston Lehner on Thursday October 29, 2015. The Class Notes belongs to MATH 256 at University of Michigan taught by Jeffrey Rauch in Fall. Since its upload, it has received 18 views. For similar materials see /class/231482/math-256-university-of-michigan in Mathematics (M) at University of Michigan.

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Date Created: 10/29/15
Math 256 Fall 2007 Professor JRauch Remarks on integrating factors 21 24 Review of the method The method of integrating factors reduces the solution of the general scalar first order linear equation y WM 905 1 to two integrations in time Here pt and gt are given continuous functions on a time interval a S t 3 Q The method relies on the product rule gem 6Atlty 14 dt Therefore if At is chosen so that then solutions of l satisfy yAty y pty 905 6140 y 6 4 got lt3gt Equation 2 is equivalent to the texts equation for lnp between equations 29 and 30 Equation 3 is equivalent to 32 in the text The analysis of y is reduced to two steps 1 Find an antiderivative At of pt as in 2 Find an antiderivative kt of CA gt Then eAtyt kt 0 W e Atkt 0 4 Examples where both antiderivatives are elementary are rare so the practice examples in the text are of necessity repetitive In class we worked the example on page 37 We found 1 CA t2 kt t4 and y 1572054 O Even when the primitives are not given by simple equations the formulas yield information about y We give two examples Solution of initial value problems Theorem 241 1

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